For very small parameter values log transform is recommended in PEST manual

Experience has shown repeatedly that log transformation of at least some parameters can
make the difference between a successful inversion process and an unsuccessful one. This is
because, in many cases, the linearity approximation on which each PEST iteration is based
holds better when certain parameters are log-transformed. It also follows from the fact that,
implied in log-transformation, is a normalization of parameters with respect to their innate
variability. The inversion process is thereby able to access, to some extent at least, the
benefits which follow from Kahunen-Loève transformation of parameters.